With Mitt Romney as the prime example of how bad the situation is for the GOP - he lost Hispanics by over 40 points to President Obama - some in the party have drawn the conclusion that the GOP's hard line on immigration is the reason for its troubles with Hispanics. In the aftermath of Romney's drubbing, several Republicans publicly called for their party to be more inclusive and some have now moved to the next stage of repairing relations with Hispanic voters - proposing legislation - despite criticism from Democrats that this push is purely political.

The Republican-led House of Representatives is taking up a measure this week that would create a new immigration program to give high-skilled workers in the science, technology engineering and math (STEM) industries permanent residency in the U.S.

Additionally, two retiring Republicans, Sens. Jon Kyl, R-Ariz., and Kay Bailey Hutchison, R-Texas, joined with fellow co-sponsor Sen. John McCain, R-Ariz., to introduce a new version of the DREAM Act legislation Tuesday. It would provide permanent residency, but not citizenship, to children under the age of 14 brought to the U.S. by their illegal immigrant parents. In exchange, the youth would have to obtain higher education or serve in the military. The measure is similar to the presidential directive issued by Mr. Obama this past summer and would lock it into federal law.

"While this legislation addresses a single facet of our nation's complex immigration problem, it is nonetheless a step forward in addressing a time sensitive issue," Kyl said.

A Senate Democratic aide said the measure means little because undocumented youth have already been given reprieve from the president. He also said it is unlikely to be brought up before the end of the year, but "it is encouraging that Republicans are willing to correct the missteps and move the debate forward" for the next Congress.

Many Republicans, until recently, were adamantly opposed to various versions of the DREAM Act, even though it was first introduced by Sen. Orrin Hatch, R-Utah., in 2001.

For example, in 2010, after the Senate failed to pass a version of the DREAM Act that included a path to citizenship, McCain said, "I cannot put the priorities of these students, as difficult and unfair in many respects as their situation is, ahead of my constituents and the American people who demand that the Federal government fulfill its Constitutional duty to secure our borders before we undertake other reforms."

Mark Kirkorian, Executive Director of the Center for Immigration Studies, a group that calls for fewer legal immigrants and strongly opposes illegal immigration, says the DREAM Act is a "compelling" issue for Republicans if they want to appeal to Hispanic voters because undocumented children are blameless innocents.

"They need to do something proactive but also address this most sympathetic group of illegal aliens," Kirkorian said.

Meanwhile, the House bill being taken up this week, the STEM Act, is authored by Rep. Lamar Smith, R-Texas, who has previously been a staunch supporter of many of the harshest immigration proposals, including notifying authorities when illegal immigrants are admitted to hospitals and doing away with birthright citizenship to children born to immigrants in the U.S.

"We cannot afford to educate these foreign graduates in the U.S. and then send them back home to work for our competitors. For America to remain the world's economic leader, we must have access to the world's best talent," Smith said in a recent statement.

But Smith's push to pass the STEM Act is viewed by some through a purely political lens, and some say his efforts are futile and misguided.

David Koelsch, immigration law professor at the University of Detroit Mercy law school, told CBS News that the timing of the bill, just weeks after an election in a Congress where 80 members won't be back come the New Year, is "truly political."

Republicans are "trying to get something done in a lame duck session to save face," he said.

The concept of the bill - increasing immigration of highly-skilled workers - is one that both sides of the aisle are able get behind because of a shortage of workers in STEM industries. It is even one of the Congressional Hispanic Caucus' priorities for comprehensive immigration reform for the upcoming Congress, but one of that caucus' leaders echoed the criticism that it's a partisan effort to send a political message.

"This week's vote is more about politics and optics for the Republicans than about anything substantive," Rep. Luis Gutierrez, D-Ill., said in a statement.

The STEM Act failed to pass the House in September because a House rule required it to pass with a two-thirds majority. Although the new rewritten version will require only a simple majority, Republicans sweetened it to appeal to Democrats by allowing family members of STEM green card recipients to wait for permanent status in the U.S. after one year.

But most Democrats are expected to oppose the measure because it cancels another program, the Diversity Visa Program, which is a lottery system allowing 55,000 residents with high school degrees of countries that have low immigration rates to apply for American residency. African residents tend to be largest recipients of the system.

"The Republicans are still looking at immigration through the old lens that legal immigration is a problem that must be eliminated or never increased," Gutierrez said. "We don't need to eliminate immigration for one group to allow immigration for another, we can and will reform immigration so that we have a controlled and legal flow that benefits the economy and keeps families together."

Even Republican allies who say the legislation is political approve of it.

"Part of the calculation is they want to be seen as putting forward substantive and practical [legislation] on immigration. If you're going to do that, this kind of targeted piecemeal measure seems to be the way to go about it," Kirkorian said.

Although the House is expected to pass the bill before the end of the week, a Senate Democratic leadership aide said the Senate will likely not address the legislation because the lame duck period between now and the end of the year is "extremely packed."